Given a semi-Hamiltonian system, we construct an F-manifold with a connection satisfying a suitable compatibility condition with the product. We exemplify this procedure in the case of the so-called ε-system. The corresponding connection turns out to be flat, and the flat coordinates give rise to additional chains of commuting flows. © 2011 Springer.
Lorenzoni, P., Pedroni, M. (2011). Natural Connections for Semi-Hamiltonian Systems: The Case of the $epsilon$-System. LETTERS IN MATHEMATICAL PHYSICS, 97(1), 85-108 [10.1007/s11005-011-0469-x].
Natural Connections for Semi-Hamiltonian Systems: The Case of the $epsilon$-System
LORENZONI, PAOLO;
2011
Abstract
Given a semi-Hamiltonian system, we construct an F-manifold with a connection satisfying a suitable compatibility condition with the product. We exemplify this procedure in the case of the so-called ε-system. The corresponding connection turns out to be flat, and the flat coordinates give rise to additional chains of commuting flows. © 2011 Springer.
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